Preheat oven to 300°F Line a 13x9 metal pan with foil, letting foil extend past edges (for ease of removal later).
Grate 2 tablespoons plus 1/2 teaspoon peel from lemons. Then squeeze 2 tablespoons plus 1 teaspoon juice. NOTE: Both the peel and juice will be divided between the shortbread and the glaze.
In food processor with knife blade attached, blend butter, granulated sugar, 1/2 cup confectioners' sugar, 2 tablespoons lemon peel, and 1 tablespoon lemon juice until creamy. (Reserve remaining lemon peel and juice for glaze). Add flour and pulse until dough begins to come together. Add cranberries and pulse until evenly mixed into dough (it's OK if all the cranberries aren't chopped). Press dough evenly into prepared pan with fingertips.
Bake 35-40 minutes or until top is pale golden and edges are very slightly browned. Cool in pan on wire rack.
When shortbread is cool, in small bowl, stir remaining 1 cup confectioners' sugar, 1 tablespoon lemon juice, and 1/2 teaspoon lemon peel until smooth, adding a little remaining juice if necessary to make a good spreading consistency. Spread glaze over shortbread. Let stand until it sets, about 30 minutes.
Using foil, transfer shortbread to cutting board. Cut lengthwise into 3 strips, then make diagonal cuts to cut each strip into 12 triangles.
Before serving, sprinkle with lemon-peel curls if desired.
Store shortbread in tightly covered container, with waxed paper between layers, at room temperature up to 4 days, or in freezer up to 3 months.